The 16 Sutras
Each sutra is a mental math technique. Tap to learn with step-by-step visual breakdowns.
By one more than the previous one
Ekadhikena Purvena
Square any number ending in 5 instantly
All from 9 and the last from 10
Nikhilam Navatashcaramam Dashatah
Find complements and multiply near bases
Vertically and crosswise
Urdhva-Tiryagbhyam
General multiplication of any numbers
Whatever the extent of its deficiency
Yavadunam
Square numbers near a base like 100
Transpose and adjust
Paravartya Yojayet
Divide using complements of the divisor
By one less than the previous one
Ekanyunena Purvena
Multiply by 9, 99, 999 using complements
Part and whole
Vyastisamastih
Use part-whole relationships to simplify
The factors of the sum equal the sum of the factors
Gunakasamuchchayah
Verify multiplication using digit sums
Differences and similarities
Chalana-Kalanabhyam
Solve quadratic equations mentally
When the sum is the same, that sum is zero
Shunyam Saamyasamuccaye
Solve equations where sums cancel out
If one is in ratio, the other is zero
Anurupye Shunyamanyat
Solve ratio and proportion problems
By addition and by subtraction
Sankalana-Vyavakalanabhyam
Solve simultaneous equations instantly
The remainders by the last digit
Sesanyankena Charamena
Find remainders using the last digit
The ultimate and twice the penultimate
Sopantyadvayamantyam
Spot number patterns and sequences
The product of the sum is the sum of the product
Gunitasamuchchayah
Verify answers using factor sums
By the completion or non-completion
Puranapuranabhyam
Find roots by completing the square